Graph Isomorphism

Definition

An isomorphism of Graph $G_1$ and $G_2$ is a Bijection $f:V_1\to V_2$ between the vertex sets of the graphs such that any two vertices $u$ and $v$ of $G_1$ are adjacent in $G_1$ if and only if $f(u)$ and $f(v)$ are adjacent in $H$. $(u,v)\in E_1\iff (f(u),f(v))\in E_2$

Is there exist an isomorphism $f$ between two graphs, the graphs are isomorphic. $G_1\cong G_2$